Problem: Solve for $x$ and $y$ using elimination. ${-2x+5y = 11}$ ${2x-3y = -1}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-2x+5y = 11}\thinspace$ to find $x$ ${-2x + 5}{(5)}{= 11}$ $-2x+25 = 11$ $-2x+25{-25} = 11{-25}$ $-2x = -14$ $\dfrac{-2x}{{-2}} = \dfrac{-14}{{-2}}$ ${x = 7}$ You can also plug ${y = 5}$ into $\thinspace {2x-3y = -1}\thinspace$ and get the same answer for $x$ : ${2x - 3}{(5)}{= -1}$ ${x = 7}$